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Graphing y =:
x^3-3x^2+2x
Identical expressions
x^ three -3x^ two +2x
x cubed minus 3x squared plus 2x
x to the power of three minus 3x to the power of two plus 2x
x3-3x2+2x
x³-3x²+2x
x to the power of 3-3x to the power of 2+2x
x^3-3x^2+2xdx
Similar expressions
x^3+3x^2+2x
x^3-3x^2-2x

Solving integrals/ x^3-3x^2+2x

Integral of x^3-3x^2+2x dx

The solution

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  2                     
  /                     
 |                      
 |  / 3      2      \   
 |  \x  - 3*x  + 2*x/ dx
 |                      
/                       
0

$$\int\limits_{0}^{2} \left(2 x + \left(x^{3} - 3 x^{2}\right)\right)\, dx$$

Integral(x^3 - 3*x^2 + 2*x, (x, 0, 2))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 x\, dx = 2 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $x^{2}$
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 3 x^{2}\right)\, dx = - 3 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $- x^{3}$
  The result is: $\frac{x^{4}}{4} - x^{3}$
The result is: $\frac{x^{4}}{4} - x^{3} + x^{2}$
Now simplify:

$x^{2} \left(\frac{x^{2}}{4} - x + 1\right)$
Add the constant of integration:

$x^{2} \left(\frac{x^{2}}{4} - x + 1\right)+ \mathrm{constant}$

The answer is:

$x^{2} \left(\frac{x^{2}}{4} - x + 1\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                       4
 | / 3      2      \           2    3   x 
 | \x  - 3*x  + 2*x/ dx = C + x  - x  + --
 |                                      4 
/

$$\int \left(2 x + \left(x^{3} - 3 x^{2}\right)\right)\, dx = C + \frac{x^{4}}{4} - x^{3} + x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

3.86683605518831e-22

3.86683605518831e-22

The graph

Use the examples entering the upper and lower limits of integration.

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Integral of x^3-3x^2+2x dx

Limits of integration:

The graph:

Piecewise:

The solution